Existence of unique solutions for perturbed autonomous differential equations

• Autores: José Ángel Cid Araújo , Rodrigo López Pouso
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 3, 2008, págs. 798-812
• Idioma: inglés
• DOI: 10.1112/jlms/jdn058
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• Resumen

  • We consider the existence of unique absolutely continuous solutions for x' = p(t)f(x) + p(t)h(t), t 0, x(0) = 0, where p, f, and h are positive almost everywhere, but none of them needs be continuous or monotone. Moreover, p and f can be unbounded around zero. Our uniqueness results are not based on assumptions on the differences f(x) � f(y), as it is usual in most uniqueness results, and they are new even when p, f, and h are continuous